How to deal with the connection between symbolic caculations and numerical caculations?

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Cola on 21 Mar 2022
Edited: Cola on 23 Mar 2022
First I need to do symbolic calculations to get the required equations. Then I use the equations for numerical calculations.
For example, I obtain the equation Ge1=-1/((2*s + 1)/(s/20 + 1) + s^2*(s/10 + 1)) by symbolic calculations.
Then If Ge1_1=-1/((2*s + 1)/(s/20 + 1) + s^2*(s/10 + 1)), one can do numerical calculations.
And I can't do numerical calculations when I want Ge1_1=Ge1.
I don't know how to deal with the connection between symbolic caculations and numerical caculations. Is there a way to solve the problem? Thank you for reading and help.
Matlab Code:
syms s
kp=(2*s+1)/(0.05*s+1);
H=1/(s^2*(0.1*s+1));
P12_1=[-1 / H - kp];
Ge1=inv(P12_1)
s=tf('s')
w=logspace(-1,1,1000);
Ge1_1=Ge1;
% Ge1_1=-1/((2*s + 1)/(s/20 + 1) + s^2*(s/10 + 1));
[mag,pha,w]=bode(Ge1_1,w);
Walter Roberson on 23 Mar 2022
P12_1=[-1 / H - kp;];
Could you confirm that you want
P12_1=[(-1 / H) - kp;];
which would be
P12_1 = (-1/ H) - kp;
??
Or did you possibly mean
P12_1=[-1 / (H - kp)];
Cola on 23 Mar 2022
Edited: Cola on 23 Mar 2022
@Walter Roberson Thanks. I mean [-1/H-kp], that is ,[(-1/ H) - kp].

Torsten on 21 Mar 2022
"matlabFunction" converts symbolic expressions into function handles for numerical calculations.
help matlabFunction
Cola on 23 Mar 2022
Edited: Cola on 23 Mar 2022
@Torsten Thank you so much.
Matlab code:
syms s
kp=(2*s+1)/(0.05*s+1);
H=1/(s^2*(0.1*s+1));
P12_1=[-1/H-kp];
Ge1=inv(P12_1);
Ge1 =
omega=logspace(-1,1,1000);
Ge1_0=matlabFunction(Ge1);
Ge1_0 = function_handle with value:
@(s)-1.0./((s.*2.0+1.0)./(s./2.0e+1+1.0)+s.^2.*(s./1.0e+1+1.0))
Ge1_1=abs(Ge1_0(1i*omega));

Paul on 23 Mar 2022
Of course, the symbolic approach will work and might even have some benefits (IDK), but just want to make sure you're aware that it's not really necessary.
% symbolic approach
syms s
kp=(2*s+1)/(0.05*s+1);
H=1/(s^2*(0.1*s+1));
P12_1=[-1 / H - kp;];
Ge1=inv(P12_1);
[num,den] = numden(Ge1);
Ge1 = num/den
Ge1 =
% control system toolbox functionality
s = tf('s');
kp=(2*s+1)/(0.05*s+1);
H=1/(s^2*(0.1*s+1));
P12_1=[-1 / H - kp;];
Ge1=inv(P12_1);
Ge1 = minreal(Ge1) % normalizes numerator and denominator for comparison to symbolic result, not necessary otherwise
Ge1 = -10 s - 200 ------------------------------------ s^4 + 30 s^3 + 200 s^2 + 400 s + 200 Continuous-time transfer function.
3 CommentsShow 1 older commentHide 1 older comment
Steven Lord on 23 Mar 2022
If you wanted to go directly from the symbolic Ge1 to the tf object Ge1 you could extract the numerator and denominator from the symbolic Ge1 with numden as you did and then convert those symbolic polynomials into vectors of polynomial coefficients with sym2poly.
syms s
kp=(2*s+1)/(0.05*s+1);
H=1/(s^2*(0.1*s+1));
P12_1=[-1 / H - kp;];
Ge1=inv(P12_1);
[num,den] = numden(Ge1)
num =
den =
N = sym2poly(num)
N = 1×2
-10 -200
D = sym2poly(den)
D = 1×5
1 30 200 400 200
You can use N and D to create the tf object.
T = tf(N, D)
T = -10 s - 200 ------------------------------------ s^4 + 30 s^3 + 200 s^2 + 400 s + 200 Continuous-time transfer function.
Cola on 23 Mar 2022
@Walter Roberson Wow，it is a cool way. I really appreciate your help.